# Trace the curve y = x / (x-1)(x+3)

Question
Analytic geometry
Trace the curve $$\displaystyle{y}=\frac{{x}}{{{x}-{1}}}{\left({x}+{3}\right)}$$

2021-03-12

We find the x-intercept of the curve
For y=o we have $$\displaystyle={0}\frac{{x}}{{{\left({x}-{1}\right)}{\left({x}+{3}\right)}}}\Rightarrow{x}={0}$$
$$\displaystyle\therefore$$ The curve touches at the point (0,0)
ext we find y-intercept of the curve
For x=0 we have y=0
$$\displaystyle\therefore$$ The curve touches the point (0)
Now, the vertical asymptotes of the curve are
$$\displaystyle{x}-{1}={0}\Rightarrow{x}={1}$$
$$\displaystyle{x}+{3}={0}\Rightarrow{x}=-{3}$$

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